arXiv research

CO-BED optimizes experiments using Bayesian methods and information theory.

Optimizes recommender selection online with D-optimal design.

We describe a general family of curved-crease folding tessellations consisting of a repeating "lens" motif formed by two convex curved arcs. The third author invented the first such design in 1992, when he made both a sketch of the crease pattern and a vinyl model (pictured below). Curve fitting suggests that this init…

Optimizes balanced treatment assignment for experiments.

New framework solves dynamic bilevel optimization problems in reinforcement learning.

Paper proposes efficient optimizers for large language models with fast convergence and low memory usage.

Accelerates policy optimization in RL with optimistic and adaptive updates.

This paper provides a general framework to study the effect of sampling properties of training data on the generalization error of the learned machine learning (ML) models. Specifically, we propose a new spectral analysis of the generalization error, expressed in terms of the power spectra of the sampling pattern and t…

A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension …

Paper studies continuous prediction with experts' advice using differential equations.

We derive a closed formula for the Heegaard Floer correction terms of lens spaces in terms of the classical Dedekind sum and its generalization, the Dedekind-Rademacher sum. Our proof relies on a reciprocity formula for the correction terms established by Ozsvath and Szabo. A consequence of our result is that the Casso…

ARO overfits by making constraints dependent on uncertainty, leading to brittleness.

Paper proposes no-regret algorithms for private GP bandit optimization.

We study the problem of finding the optimal dosage in early stage clinical trials through the multi-armed bandit lens. We advocate the use of the Thompson Sampling principle, a flexible algorithm that can accommodate different types of monotonicity assumptions on the toxicity and efficacy of the doses. For the simplest…

An emerging problem in trustworthy machine learning is to train models that produce robust interpretations for their predictions. We take a step towards solving this problem through the lens of axiomatic attribution of neural networks. Our theory is grounded in the recent work, Integrated Gradients (IG), in axiomatical…

Machine learning methods have had spectacular success on numerous problems. Here we show that a prominent class of learning algorithms - including Support Vector Machines (SVMs) -- have a natural interpretation in terms of ecological dynamics. We use these ideas to design new online SVM algorithms that exploit ecologic…

A simple model explains deep learning phenomena like grokking and gradient boosting.

Survey and clarify manifold-supported data in deep generative models.

Combines BO with context to optimize binary feedback.

We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in the class of all lens spaces.

Study spectral analysis on lens spaces, proving isospectral lens spaces with prime order fundamental groups.

Klein bottle embeds into specific lens spaces.

We give criteria for an invariant of lens space links to bound the maximal self-linking number in certain tight contact lens spaces. As a corollary we extend the Franks-Williams-Morton inequality to the setting of lens spaces.

The paper identifies knots in specific lens spaces based on their complements.

This work analyzes Batch Normalization through convex optimization, providing insights and improved training methods.

Defines spectral selectors on lens spaces for contactomorphisms.

Characterizes Legendrian knots in lens spaces.

Corrects classification of Seifert fibrations for lens spaces with non-orientable bases.

The paper reformulates an invariant and calculates it for lens spaces.

Determines conditions for ribbon cobordisms between lens spaces.

The notion of a layered triangulation of a lens space was defined by Jaco and Rubinstein in earlier work, and, unless the lens space is L(3,1), a layered triangulation with the minimal number of tetrahedra was shown to be unique and termed its "minimal layered triangulation." This paper proves that for each integer n>1…

Ozsváth-Szabó proved the property that any coefficient of Alexander polynomial of lens space knot is either $\pm1$ or $0$ and the non-zero coefficients are alternating. Combining the formulas of the Alexander polynomial of lens space knots due to Kadokami-Yamada and Ichihara-Saito-Teragaito, we refine Ozsváth-Szabó's p…

Sharp bounds on ERM's minimal error in regression.

In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. We also prove that any lens space admits only finitely many tight contact structures.

Third coefficient of lens space knots' Alexander polynomials restricts surgeries to specific torus knots.

Study contact structures on lens spaces, classifying rational knots.

We determine all the Q-fundamental surfaces in $(p,1)$-lens spaces and $(p,2)$-lens spaces with respect to natural triangulations with $p$ tetrahedra. For general $(p,q)$-lens spaces, we give an upper bound for elements of vectors which represent Q-fundamental surfaces with no quadrilateral normal disks disjoint from t…

This paper classifies minimal fillings of lens spaces.

A study on optimizing self-attention in tabular data using Optimal Transport.

We determine lens surgeries (i.e.\ Dehn surgery yielding a lens space) along the $n$-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) $n=1$ (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interes…

We determine the non-null homologous knots in lens spaces whose exteriors contain properly embedded once-punctured tori. All such knots arise as surgeries on the Whitehead link and are grid number 1 in their lens spaces. As a corollary, we classify once-punctured torus bundles that admit a lens space filling.

In this paper, we consider which lens spaces are obtainable by Dehn surgery described by Berge on doubly primitive knots. It is given an algorithm to decide whether a given lens space is obtainable by such surgery. Also included is a complete characterization of such surgery yielding lens spaces with Klein bottles.

New proof of Alexander polynomial constraints for lens space surgeries.

We show how the Alexander polynomial of links in lens spaces is related to the classical Alexander polynomial of a link in the 3-sphere, obtained by cutting out the exceptional lens space fibre. It follows from these relationship that a certain normalization of the Alexander polynomial satisfies a skein relation in len…

In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens space is introduced. It is proved that if two lens spaces are isospectral then the d…

We describe an effective algorithm for computing Seiberg-Witen invariants of lens spaces. We apply it to two problems: (i) to compute the Froyshov invariants of a large family of lens spaces; (ii) to show that the knowledge of the Seiberg-Witten invariants of lens spaces is topologically equivalent to the knowledge of …

Researchers create crystallizations of lens spaces.

Study on lens spaces bounding 4-manifolds with specific Betti numbers.